Comment on 'Nonlinear eigenvalue problems'

被引：5

作者：

Kerr, Oliver S. ^{[1
]}

机构：

[1] City Univ London, Dept Math, London EC1V 0HB, England

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2014年 / 47卷 / 36期

关键词：

asymptotics; eigenvalues; ordinary differential equations;

D O I：

10.1088/1751-8113/47/36/368001

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The asymptotic behaviour of solutions to y'(x) = cos [pi xy(x)] was investigated by Bender et al (2014 J. Phys. A: Math. Theor. 47 235204). They found, for example, a relation between the initial valuey(0) = a and the number of maxima that the solution exhibited. We present an alternative derivation of the asymptotic results that looks at the solutions in the regions x < y and x > y, and confirms the behaviour found previously for larger values of a. This method uses the small amplitude and high frequency of the oscillatory behaviour in the region x < y.

引用

页数：5